-- then the answer is obvious. Just as 1 apple is half of 2 apples, so

1-fifth is half of 2-fifths.

Example 10.

37

is half of what number?

Answer.

37

is half of

67

.

Example 11.

37

is a third of what number?

Answer.

37

is a third of

97

, which is 1

27

.

Example 12. To make an orange dye, 3 parts of red dye are mixed with 2 parts of yellow dye. To make a green dye, 2 parts of blue dye are mixed with 1 part of yellow dye. If equal amounts of orange and green are mixed, what fraction of the new mixture is yellow dye?

Solution. For convenience, let

O = Orange dye, R = Red dye, Y = Yellow dye,

G = Green dye, B = Blue dye.

Now, the orange dye consists of a total of five parts: 3 parts red and 2 parts yellow. That is,

O

=

35

R +

25

Y.

The green dye consists of three parts: 2 parts blue and 1 part yellow.

G

=

23

B +

13

Y.

To add equal amounts of O and G, we may simply add half of each. Therefore, half of O is

O

=

3 10

R +

15

Y.

And half of G is

O

=

13

B +

16

Y.

Upon adding those equal parts of O and G, the new mixture will consist of